Your investment firm just got two new clients. Bob placed $12,000 in a short-term, high-risk investment backing a pharmaceutical startup, while Carol placed $20,000 in a long-term, safer investment using index funds. If Bobs investment is successful, he stands to gain 9% per year. Carols investment is less likely to fail, but will only return 4% per year. If both investments succeed, how long will it take for the value of Bobs investment to catch up to Carols?